Berilgan sig‘imlar nisbati C1 = C2 = C3/2 = mkF, shu jumladan, C2 = C1/2 = mkF va C3 = 4 mkF

30-masala
Berilgan sig‘imlar nisbati C1 = 2C2 = C3/2 = 2 mkF, shu jumladan, C2 = C1/2 = 1 mkF va C3 = 4 mkF.

Zanjir ulangan bo‘lganligi uchun, sig‘imlar ulash shartini qo‘llaymiz:

1/C_eq = 1/C1 + 1/C2 + 1/C3

1/C_eq = 1/2 + 2 + 1/4

1/C_eq = 9/4

C_eq = 4/9 mkF

Shu bilan, zanjiming ekvivalent sig‘imi:

C_eq = ε_0 * ε_r * A/d

bu yerda ε_0 - elektr maydon vakuumdagi permittivitet, ε_r - material permittiviteti, A - plochkani yuzasi, d - zanjirning o‘rta masofasi.

Berilgan parametrlar bo‘yicha, zanjirning o‘rta masofasini hisoblaymiz:

C_eq = ε_0 * ε_r * A/d

d = ε_0 * ε_r * A / C_eq

d = (8.85*10^-12 * 1 * (1*0.001)) / (4/9*10^-15) = 19.63 mm

Shu bilan, zanjirning o‘rta masofasi 19.63 mm.

Kuch uchun shakl topish uchun, uy bilan sayohat qilamiz. Zanjir uchun kuch formulasi:

P = V^2 / R = V * I

bu yerda R - zanjirining rezistansi, V - zanjirning uchkana kuchi, I - zanjirdan o‘tgani oqim kuchi.

Zanjir ulanganligi uchun, R ni quyidagi formula bilan hisoblaymiz:

1/R = 1/R1 + 1/R2 + 1/R3

R1 = 1/(ω*C1) = 1/(2π*400*2*10^-6) ≈ 0.994 kOhm

R2 = 1/(ω*C2) = 1/(2π*400*1*10^-6) ≈ 2.486 kOhm

R3 = 1/(ω*C3) = 1/(2π*400*4*10^-6) ≈ 0.622 kOhm

1/R = 1/R1 + 1/R2 + 1/R3 ≈ 1.832 kOhm

R ≈ 0.545 kOhm

Kuch uchun ko‘rsatma hisoblanadi:

P = V * I = V^2 / R ≈ (220)^2 / 0.545 ≈ 89238.5 W

Shu bilan, zanjirdagi tok:

I = P / V = 89238.5 / 220 ≈ 405 A

Javob: Zanjiming ekvivalent sig‘imi 4/9 mkF bo‘lib, ulangan zanjirning o‘rta masofasi 19.63 mm, zanjirdagi kuch 89238.5 W va tok 405 A